Something I've never understood about non-inertial reference frames

[Vorde]

Basically: I jump forwards, exerting an amount of energy enough to push me forward with some velocity.

But in my reference frame, I exert the same force, except the entire universe moves backwards with that same velocity, where did that energy come from?

I sort of know this has to do with fictitious forces, but I'm not sure how.

Thanks.

 

[cepheid]

I'm not sure about your jumping example. For me one way of looking at non-inertial reference frames is kind of like this (but I'm open to critiques from people):

Say you're on bus. You and everyone else in the bus, (and the bus itself), are happily sitting around stationary, while the entire rest of the world streams backwards past you at a constant speed. You notice that the driver puts his foot down, depressing a pedal on the floor. At this point, you feel a force throwing you forward in your seat. You look out the window and notice that, although the outside world is still streaming backwards past you, it is not doing so as quickly as it was before. In fact its rearward motion is slowing. If its backwards speed decreased, then it must have been experiencing a forward acceleration. What provided this forward acceleration to the outside world? Why, it was the very same forwards force that just suddenly appeared and threw you forward in your seat!

Where did this magical "sideways gravity" come from? Who knows? But you must take it into consideration in order for Newton's laws to still appear valid to you, and it certainly felt real enough to you...

 

[The_Duck]

Yes, it's the fictitious forces. In non-inertial reference frames, there generally appear bizarre forces. For example, in rotating reference frames, everything becomes subject to the centrifugal and Coriolis forces in addition to the familiar forces of gravity, electromagnetism, etc. These new forces are strange beasts that, like gravity, are proportional to mass, but depend on the position and velocity of the objects they act on in a way very different from gravity. For example the centrifugal force is like a gravitational field that points radially *outward* from the origin and has a magnitude proportional to your distance from the origin. Similarly in a linearly accelerating reference frame there appears a force that looks like a uniform gravitational field permeating the universe, which starts accelerating everything else in the universe backwards.

Inertial reference frames can be *defined* to be the reference frames free of these strange forces, in which the laws of mechanics take their simplest form.

 

[Vorde]

Ok, I assumed that something like this was the explanation but didn't have a firm grasp. Thank you, to both of you.

 

[PJC01]

I can understand your confusion about non-inertial reference frames and the concept of fictitious forces. Let me try to explain it in a simple way.

In your example, when you jump forward, you exert a force on the ground which pushes you forward with a certain velocity. In this scenario, you are in an inertial reference frame, meaning there are no external forces acting on you and you are moving at a constant velocity.

However, if we consider a non-inertial reference frame, where the entire universe is moving backwards with the same velocity as you, then the situation is different. In this frame, you are not at rest and there are external forces acting on you. These external forces are known as fictitious forces.

Fictitious forces are not real forces, but they appear to exist due to the acceleration of the reference frame. In this case, the fictitious force is the force that appears to push you backward when you jump forward. This force is not coming from anywhere, it is simply a result of the acceleration of the reference frame.

To understand this concept better, think of being in a car that is accelerating forward. If you throw a ball forward, it will appear to move in a curved path from your perspective inside the car. This is because the car is accelerating and the ball is experiencing a fictitious force pushing it backward. However, an observer outside the car would see the ball moving in a straight line.

In summary, the energy you use to jump forward does not change in a non-inertial reference frame, but the appearance of the motion and forces may be different due to the acceleration of the reference frame. I hope this helps clarify your understanding of non-inertial reference frames and fictitious forces.